lateral-torsional buckling of tapered i-beams

[Anonymous]

Hello!

I am wondering how to calculate the critical moment for an cantilever tapered beam.

We use EC. And they dont state how to deal with this sort of problem. 

I calculated the critical moment for the biggest crossection. Is this wrong?

[mathias_peron]

Hi Bertil,

Yes it is wrong as your section modulus is variable along the beam. 

A very conservative approach would be to calculate MCr with the smallest section to be 200% sure your beam is not failing.

What you can do to get the real MCr of your tapered beam is to model it with shell elements, carefully consider your boundary conditions (supports) and run a buckling analysis. It will extract for you the MCr you are looking for.

Have a nice day,

Mathias.

[Anonymous]

Thanks for the info.

Robot calculates the average crossection and i get an reduced moment of 1600kNm. (nearly 9000kNm when not considering  lateral-torsional buckling) 

I found that very conservative. Maybe my boundery condions are all wrong?. 

The beam crossection are: tw=25 tf=30 hw=1300 (400@end) Braces are located at end. 

Can you help me out? 🙂 I will try to model a shell element, but i am not that familiar with robot. (former user of STADpro)

[mathias_peron · Accepted solution]

No worries it is very easy to do.

1 - Model your beam in the shell design module of Robot (geometry/material/boundary conditions)

2 - I assume the beam is loaded with a UDL -> apply a load of 1kN/m on the top flange using a surface load (1 kN/m / width of top flange)

3 - Change your analysis type to Buckling (with a small number of modes)

4 - Run the analysis

5 - Get the buckling mode that interests you with diagrams for bars/deformation and mode n#

5 - Go to Results/Advanced/Critical load to get the load multiplier of your buckling mode

The critical multiplier is your MCr.

Have a nice day,

Mathias.

[Anonymous]

Thanks for the great step to step!

I modelled the beam. And defined a surface load of 1kpa/0.3m load. But my mulitipliers is getting very high. (i hold the top flange in y-directiopn due to the roof. Mode 2 shows the lateral buckling of the lower flange.

[Anonymous]

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[mathias_peron]

Hi,

Sorry what I mean is that the critical coeff is the load leading to MCr, not MCr itself.

But your value seem correct to me. 149 kN/m is the load leading to MCr.

Try to better mesh the beam just to see if you can get a better results. But it all seems good to me 😉

Have a nice day!

Mathias.

[Anonymous]

Thanks alot!

This helps me determine special cases not directly coverd by the Eurocodes.!

[Anonymous]

LTB equations assume that beams are restrained from rotation at the ends.

Add horizontal supports at the top flanges on both supports and you will have your "more realistic" result.